Time reversal filters are used for processing both audio and video signals. For spatially filtering images, a separable filter, such as a Gaussian filter, is particularly desirable. Each horizontal scan line of pixels is filtered independently, then each vertical column of pixels is similarly filtered. If the filter is a true Gaussian filter, then the resulting filtering of the two dimensional image is radially symmetric. That is, at any arbitrary angle through the image, the resulting filtered image will be the same as if the line of pixels at such arbitrary angle were directly filtered by the Gaussian filter. To the extent that a close approximation to Gaussian filter is used, the resulting image filtering is close to radially symmetric. Due to its symmetry, the ideal Gaussian filter has no phase shift over all frequencies of interest.
One of the most important applications of Gaussian filtering is for sharpening, or edge enhancement. Gaussian filtering to sharpen an image is especially desirable when a photographic original has been scanned at very high resolution (for example, a 35 mm negative scanned at 4000 dots per inch). Scanning an image at very high resolution, i.e. significantly greater than that absolutely needed to capture the image detail within the Nyquist frequency of the sampling process, then sharpening using Gaussian filtering, produces an image with minimal image artifacts. The rotational symmetry of the Gaussian filter means that lines of any angle will be sharpened by an identical amount, a property not shared by the closest competitor to the Gaussian filter for image sharpening: the Laplacian (or 3.times.3 convolution) filter. Thus, the Gaussian filtering is popular for very high quality image processing systems.
Another application of Gaussian filtering is removing film grain, unwanted screens (as when scanning photos from a magazine), as well as other unwanted artifacts.
A drawback to Gaussian filtering is its relatively great computational cost. Most digital implementations of a Gaussian filter use finite impulse response (FIR) filters. The larger the extent, or, equivalently, the lower the cutoff frequency of the Gaussian filter, the more computationally expensive it is to implement. A typical implementation requires dozens of multiplications per pixel. Further, because the shape of the Gaussian curve is infinite in extent, practical implementations must truncate the actual curve, which can cause quality problems.
Time reversal filtering is known in the field of audio engineering. The input audio signal is filtered through a first stage, and the result recorded on tape. Then, the tape is played back backwards (i.e. in reverse) through a second, identical stage of filtering. The result is recorded on a second tape. When the second tape is played back again backwards, the result is the desired filtered audio signal. Symmetrical filtering is desired in the field of audio processing. The result of symmetrical time reverse filtering is an audio signal in which the frequencies have been filtered as desired, but the phase has been absolutely preserved.
There are many drawbacks to audio time reversal filtering. For one, it takes twice as long, because the tape must be run through a second time. For another, it requires twice as much tape. Further, the signal undergoes the degradation of two recording processes, which is a much more severe problem for analog than digital recording. Perhaps most importantly, it is completely unworkable for real time audio processing, because it is impossible to hear any results until the whole tape has been filtered.